Extended Mixed AKNS-Lund-Regge Model and Its Self-similarity Reduction - Ruy, D.V.; Melo, G.R. de (Discontinuity, Nonlinearity, and Complexity, 2026)
We discuss the relation between the self-similarity reduction of the generalized mixed mKdV-sinh-Gordon model and the fourth-order equation obtained by Kudryashov inJ. Phys. A: Math. Theor.35(2002) 93-99. Also, it is shown two particular solutions for this equation. Then, we extend the mixed AKNS-Lund-Regge model and study its self-similarity reduction. We obtain thefifth Painlevé equation as a particular case of this reduction and a fourth-order second-degree equation otherwise. The relation between a integrable model and a fourth-order second-degree equation is interesting because the general solution of this equation must have the Painlevé property due the Ablowitz, Ramani and Segur conjecture.